Enhanced Redox Electrocatalysis in High-Entropy Perovskite Fluorides by Tailoring d–p Hybridization

Highlights The tailored KCoMnNiMgZnF3-HEC cathode delivers extremely high discharge capacity (22,104 mAh g−1), outstanding long-term cyclability (over 500 h), preceding majority of traditional catalysts reported. Entropy effect of multiple sites in KCoMnNiMgZnF3-HEC engenders appropriate regulation of 3d orbital structure, leading to a moderate hybridization with the p orbital of key intermediate. The homogeneous nucleation of Li2O2 is achieved on multiple cation site, contributing to effective mass transfer at the three-phase interface, and thus, the reversibility of O2/Li2O2 conversion. Supplementary Information The online version contains supplementary material available at 10.1007/s40820-023-01275-3.


This work
Computational simulations: Based on COMSOL Multiphysics 6.0 software, we simulated two types of Li2O2 deposition behavior on O2-electrode.The twodimensional phase field model of the O2-electrode microenvironment is constructed by coupling different modules of electrochemistry, dilute material transfer, solid mechanics field, domain ordinary differential and differential algebraic equations.In the whole process, considering the anisotropic surface energy, we introduced a thermodynamic framework through data transmission.The operational details were shown as following.
Nano-Micro Letters S8/S15 (2) Li2O2 accumulates on the active surface of the porous electrode.
(4) Temperature changes during discharge process are not considered.
(5) The electrolyte is a uniform organic solvent mixture.
(6) The mass transfer process only include diffusion and electromigration, and ignore convection effect.
(7) The diffusion of Li + follows the concentrated solution electrolyte theory.
(8) O2 is dissolved in the electrolyte with saturated concentration.
(9) The reactant supply is adequate and stable during discharge process.

Establishment of model:
The establishment of mathematical model for electrode microenvironment is based on local assumption principles.
(a) The discharge process is described by the following equation: The electrochemical reaction rate (Re) is described by the following equation: Where k0 is the reaction rate constant, αc is the cathode charge transfer coefficient, αa is the anode charge transfer coefficient, η is the overpotentials, ci is the concentration, R is the ideal gas constant, T is the temperature, F is Faraday's constant (F= 96487 C/mol), n is the number of electrons transferred.
(c) The overpotential is described by the following equation: Where Φ is the reaction potential, Φeq is the reaction equilibrium potential.
(d) The change of phase field is described by the following equation: Where ξ is the phase field, associated with the dimensionless concentration of Li2O2.
(e) The effective diffusion coefficient (D eff ) is described by the following equation: Where D e is the diffusion coefficient of cathode, D s is the diffusion coefficient of Nano-Micro Letters S9/S15 electrolyte (f) The change of concentration is described by the following equation: Where cmax, Li2O2 is the saturation concentration of Li2O2.
(g) The occupation ratio of porosity for Li2O2 is described by the following equation: The formation rate of Li2O2 is described by the following equation: Where Ni is the molar flux, ci is the volume concentration, ri is the formation rate from solid to liquid.

The set of coundary conditions:
The established two-dimensional phase field geometric model mainly included porous electrode surface, interfacial double layer and organic electrolyte, as shown in Fig. S11.The detailed parameters were listed as following (Table S7).

Grid division of two models:
In COMSOL Multiphysics, the model grid was set up by controlling the physical field.The model was mesh-divided though a free triangle mesh, in which the mesh precision was ultra-refined, contaning 139028 domain units and 1822 boundary units.The errors at the grid level were controlled within the acceptable range.
According to the distribution of catalytic site distributions and morphology of intial Li2O2 (Fig. 5a, e), we built two types of grid division, as shown in  In-situ DEMS measurement: A customized Swagelok-type Li-O2 cell was used in this study, with two PEEK capillary tubes serving as purge gas inlet and outlet.A speciallydesigned gas-purging system was utilized to connect the Li-O2 cell to a commercial magnetic sector mass spectrometer (Qulee, QCS-ULVAC).The flow rate of purge gas was controlled by a digital mass flow meter (Bronkhorst).During the discharging process, a mixture of Ar/O2 (molar ratio 1/4) with a flux of 5 mL min -1 was used as the working gas for the purpose of quantifying O2 consumption.During the discharging process, high-purity Ar was used as the carrier gas.In either case, Ar was included as an internal trace gas with a known invariable flux to ensure accurate measurement.The DEMS cell assembly resembled that mentioned in the electrochemical measurements part.In terms of the discharge and charge conditions, all cells were discharged/charged at a constant current of 1000 mA g -1 , with the capacity being limited to 1000 mAh g -1 .
These parameters were carefully selected to ensure reliable and consistent performance in the Li-O2 cells, facilitating accurate characterization of the electrochemical reactions.The ratio of transferred charge to O2 production was calculated by the following equation: Table S9 The calculated electron spin states of KCoF3

Fig. S14
Fig. S14 The grid division structure diagram of model I with KCoF3 Fig. S18 In-situ DEMS curves of LOB with KCoMnNiMgZnF3-HEC during 1st discharging process

Table S2 The
Gibbs free energy of each endothermic step through different reaction pathways on site of Co in KCoF3, Mn in KMnF3, Ni in KNiF3, Mg in KMgF3, Zn in KZnF3

Table S3
Gibbs free energy of each endothermic step through different reaction pathways on site of Co*, Ni*, Mn*, Mg*, Zn* in KCoMnNiMgZnF3-HEC

Table S6
The corresponding fitted resistance value at different discharge/charge stages Table S7 Performance comparison for other representative published efforts

Table S8
Parameters in two-dimensional (2D) transient model

Table S10
The calculated electron spin states of KCoMnNiF3

Table S12
The calculated electron spin states of KCoMnNiZnF3

Table S13
The calculated electron spin states of KCoMnNiMgZnF3-HEC

Table S14
The Gibbs free energy of each endothermic step through different reaction pathways on Co sites in KCoF3, KCoMnNiF3, KCoMnNiMgF3, KCoMnNiZnF3, KCoMnNiMgZnF3-HEC